quadric

/'kwɔdrik/

Thân thiện

A student graphs a quadric on a coordinate plane.

Definition

1. Noun:
   • A curve or surface whose equation (in Cartesian coordinates) is of the second degree: In mathematics, a "quadric" is a geometric shape, such as a curve in two dimensions or a surface in three dimensions, defined by a polynomial equation where the highest sum of exponents in any term is two.

Examples of Usage

• Noun:
  • The sphere and the ellipsoid are common examples of a quadric surface.
  • In algebra, we learned to classify conic sections, which are types of quadric curves.

Advanced Usage

• "Quadric surface": A specific term for a three-dimensional quadric.

  • The paraboloid is a quadric surface used in the design of satellite dishes.

• "Degenerate quadric": A quadric that simplifies into a lower-dimensional shape, like a pair of lines or a single point.

  • When the discriminant is zero, the equation may represent a degenerate quadric.

Variants and Related Words

• Quadratic (adj): Pertaining to the second degree or involving terms up to the square of a variable.

  • A quadratic equation is related to the concept of a quadric curve.

• Quadric cone (n): A specific quadric surface shaped like a double cone.

  • The equation x² + y² - z² = 0 defines a quadric cone.

• Quadric cylinder (n): A quadric surface that extends a two-dimensional conic section along an axis.

  • A parabolic cylinder is a type of quadric cylinder.

Synonyms

• Second-degree surface/curve: A descriptive synonym emphasizing the defining polynomial degree.
• Conicoid: A less common term, especially for quadric surfaces.

Related Idioms or Phrases

(This term is highly technical and specific to mathematics; it is not commonly used in idiomatic expressions or phrasal verbs.)

Học thuật

Noun

1. a curve or surface whose equation (in Cartesian coordinates) is of the second degree

Từ đồng nghĩa

• quadric surface